Are you talking about paying property taxes via an escrow account that your mortgage lender takes care of for you? That's not your "mortgage payment", which is a function of your loan size, interest rate, and term, and nothing more. The monthly mortgage payment (assuming same term and interest rate) is the same in CA and TX for the same amount of loan.
(I guess we could also talk about things like PMI, but that won't raise your payment by all that much.)
Property taxes might be quite a bit higher in TX, but I'm not convinced a $900k home in TX is the equivalent to a $1.2-1.3M home in CA. I would expect that's closer to $1.7-2M, and then the property tax amounts end up being not that different.
From there tax basis more or less tracks market value, but it’s possible to protest the assessor to keep it below market value (though it’s time intensive and requires in-person hearings).
To get ahead of any artificial attempts at deflating tax basis, Dallas also maintains a comprehensive public lot value database that assigns a land value for tax purposes based on census tract (initially likely a product of redlining, but now based on average census tract market value) — so, similar to a pure land value tax, even if you’re sitting on an unimproved piece of land, you’ll still be taxed similar to the average home in the neighborhood, which has the effect of setting a tax floor.
Austin is similar, I believe. Most cities have to, as aside from sales tax property tax is their only source of revenue, because any sort of income tax is constitutionally banned.
No income tax, but property taxes are at least 2% of the assessed value, and sometimes 3. You'll see that on the Zillow listing.
But ultimately it seems like they get you one way or another, through sales, Income, and or property tax.